Rt Revd Michael Campbell took offence to the message from Philip Bannister who was raising concern about a decision to close two churches.
In the note he said he doubted whether the bishop would actually read his words and was expecting his secretary to provide a response.
Bishop Michael said this was a 'most serious - and defamatory - allegation'.
Mr Bannister has since issued a public apology which has been quoted in the Lancashire Evening Post. He said: "I never meant to hurt anyone.
"Looking at it I was probably a bit harsh.
"It was probably an error of judgement on my part and I've been given a slap down."
Tensions have been running high in the region following the decision to close St Ignatius and St Augustine's in Preston. A shortage of priests has been cited as the reason.